Tracking Control Of Nonlinear Constrained Systems Via Function Transformation Approach

Affected by the physical limitations of its components and the external environment,the output and states of the system are required to satisfy certain constraints,i.e.,they need to be ensured within a specific range during the system operation,which brings challenges for control design and analysis.Besides,the performance of the controlled system is an important evaluation index for the effectiveness of the controller,which is easily affected by uncertain terms,external disturbances and constraints.Nowadays,although some research results have been presented on the control of uncertain constrained nonlinear systems,there are also some problems to be solved.In this paper,by using the function transformation technique together with other skills,we focus on improving the performance,of constrained systems,extending the application of constrained control and reducing the communication burden for nonlinear systems with output or state constraint.The main tasks and innovations are as follows:(1)The problem of accelerated tracking control for a class of nonlinear systems with output constraint is investigated.First,to analyze and design the convergence rate,the concept of rate function is introduced,with which a convergence rate transformation function is constructed.Then,by using rate function transformation for the tracking error,the transient performance and steady-state performance of the first-order system are analyzed with the help of an accelerated dynamic model.Finally,for the output-constrained high-order nonlinear system,a Barrier Lyapunov function(BLF)is constructed based on the speed function transformation,then a robust adaptive controller is designed based on the backstepping technique.The tracking error is ensured to converge to the specified tracking accuracy with preset speed.(2)The practical tracking control is investigated for a class of pure-feedback systems subject to asymmetric time-varying state constraints.Different from the traditional methods based on BLF or Integral Barrier Lyapunov function(i BLF),which need to transform the state constraint problem into the error constraint problem,a new constraint transformation function is constructed to implement constraints on errors and states of the system directly.It is proven that the feasibility conditions can be avoided for design virtual controller when combining the backstepping technique.On the other hand,to improve the tracking accuracy,an exponential proportional function is introduced to transform the tracking error.The designed practical tracking controller ensures that not only the system states are within the constraints for all time,but also the tracking error converges to an arbitrarily small neighborhood of zero.Besides,by choosing different scale functions,three different tracking effects can be obtained,i.e.,ultimately uniformly bounded tracking,practical tracking,and asymptotic tracking.(3)The practical finite-time tracking control is investigated for nonlinear systems with state constraints.In existing finite-time control methods,the designed controllers are based on the fractional power of the system states or error,which leads to non-smooth control signals,together with complex control design and stability analysis.Different from most existing results,a new method is proposed to guarantee practical finite time stability.First,the concept of convergence time regulator(convergence time adjustment function)is introduced for Euler-Lagrange systems with position and velocity constraints,based on which the performance function is constructed.The prescribed tracking accuracy is able to be achieved within given time as long as the tracking error is with the performance constraints.Then,combining neural network(NN)and dynamic surface(DSC)technique,an adaptive controller is designed based on conventional state(angular position and angular velocity)feedback.Finally,the practical finite-time control is extended to the high-order nonlinear strict feedback systems with state constraints.It is proven that the states of the system obey the constraints at all times,and the tracking time and tracking accuracy can be set in advance as needed.(4)The tracking control problem of a class of pure feedback systems is investigated under the condition of constrained and unconstrained alternately.Note that the existing control strategies for handling constraints can only cope with the case with constraints.However,during the system operation,the constrained cases and unconstrained cases usually alternate.In order to deal with constrained and non-constrained problems in a unified way,a new and more general constraint transformation function is constructed.By transforming the original system states,new state variables are formed,where the original state constrained problem is transformed into the boundedness of new state variables for constrained cases and new state variables are equivalent to the original system states for unconstrained cases.Therefore,this constraint transformation method can be adapted to both constrained and unconstrained cases at the same time.It is proven that the designed robust adaptive control algorithm can not only deal with constrained and unconstrained situations uniformly,but also avoid the feasibility conditions.(5)The problem that how to design control algorithms to reduce the communication burden of the systems with output or state constraints is investigated.In the network control systems,the bandwidth of the channel for signal transmission is limited.When the signal transmission is frequent,it may occur signal blocking and packet loss,which will affect the performance of the system.For a class of nonlinear pure feedback systems,an event-triggered control algorithm is designed,where control signals transmission are no longer at a fixed period,but based on the designed triggering conditions.In this way,the signal transmission frequency is reduced greatly.In order to avoid the assumption that the system is input to state stable,a continuous indirect control variable is introduced.Besides,At the same time,an adaptive controller and corresponding event triggering conditions are designed simultaneously to compensate for sampling errors caused by the discontinuous transmission of control signals.It is proven that the output or states of the system can be guaranteed within the constraint boundary,and the communication burden is reduced at the same time due to the intermittently transmitted control signals.